Question

while visiting her grandparents, kendall found a box with a surprising number of spare keys. kendall figured that the color of the sticker on each key must indicate what the key was for. when kendall tested the keys, she was surprised to find that this was not the case. what is the probability that a randomly selected key is labeled with a green sticker and does not open the back door of the house? simplify any fractions.

Explanation:

Step1: Calculate the total number of keys

Add up all the values in the table: \(6 + 9+11 + 4+7 + 12=\sum_{i = 1}^{6}x_{i}=49\)

Step2: Find the number of keys with green sticker and not for back - door

The number of keys with green sticker and not for back - door is the value in the "Green sticker" row and "Front door of the house" column, which is \(11\)

Step3: Calculate the probability

The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P=\frac{11}{49}\)

Answer:

\(\frac{11}{49}\)